Former Liberal staffer Brittany Higgins says she was sexually assaulted by a colleague in a minister's office in 2019.

Three other women have come forward to accuse the same man of sexual assault.

Prime Minister Scott Morrison and Defence Minister Linda Reynolds are under pressure to justify the government's response to the incident.

Former Liberal MP Sharman Stone has vowed to keep pursuing the issue, which she says centres on an endemic toxic culture in politics.

"This has to be a circuit breaker. We Liberal women, I'm still a member of the party, no longer a member of parliament, we are not going to let this go," she told Sky News.

Dr Stone said the four inquiries announced by the prime minister appeared a chaotic and knee-jerk political response.

"I'm worried it will be a quick and dirty 'let's show we've got an outcome with 43 recommendations for each and we'll get back to you'."

Department of Prime Minister and Cabinet secretary Philip Gaetjens is looking into when the prime minister's office knew about the alleged rape of Ms Higgins.

Mr Gaetjens was Mr Morrison's chief of staff between 2015 and 2018.

Government Senate leader Simon Birmingham is working with parties from across the political divide on an investigation into the workplace culture of parliament.

Mr Morrison said he expected the findings would be made public after a quick but thorough inquiry.

Liberal MP Celia Hammond's review of Liberal Party culture will be absorbed into the cross-party probe.

But the prime minister is refusing to say whether the Gaetjens review of his own office will be released until he reads its contents.

Labor leader Anthony Albanese has called for the review to be made public while also criticising the independence of the former senior Liberal staffer.

"After sports rorts I have zero confidence in any process led by Phil Gaetjens," Mr Albanese told a caucus meeting.

Mr Morrison denies he sees the issue as a distraction.

"I wouldn't accept that suggestion for a second. They're important issues and we are addressing them," he told reporters.

The Greens are pushing for the cross-party inquiry to be conducted by Sex Discrimination Commissioner Kate Jenkins with input from former staffers.

Cabinet minister Greg Hunt is confident the multiple inquiries will achieve results.

"There will be very clear change and they will be improved systems, and I think that that's an important thing," he said.

Cabinet minister Michaelia Cash, who employed Ms Higgins after the May 2019 election, insists she wasn't told the incident was an alleged sexual assault.

In October, a media query about the incident was lodged with Senator Cash's office.

"She was very concerned that she was going to become a story. It was actually about her job and nothing more," Senator Cash said.

Australian Associated Press